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Simplifying x(9x + 41) = 240 Reorder the terms: x(41 + 9x) = 240 (41 * x + 9x * x) = 240 (41x + 9x2) = 240 Solving 41x + 9x2 = 240 Solving for variable 'x'. Reorder the terms: -240 + 41x + 9x2 = 240 + -240 Combine like terms: 240 + -240 = 0 -240 + 41x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -26.66666667 + 4.555555556x + x2 = 0 Move the constant term to the right: Add '26.66666667' to each side of the equation. -26.66666667 + 4.555555556x + 26.66666667 + x2 = 0 + 26.66666667 Reorder the terms: -26.66666667 + 26.66666667 + 4.555555556x + x2 = 0 + 26.66666667 Combine like terms: -26.66666667 + 26.66666667 = 0.00000000 0.00000000 + 4.555555556x + x2 = 0 + 26.66666667 4.555555556x + x2 = 0 + 26.66666667 Combine like terms: 0 + 26.66666667 = 26.66666667 4.555555556x + x2 = 26.66666667 The x term is 4.555555556x. Take half its coefficient (2.277777778). Square it (5.188271606) and add it to both sides. Add '5.188271606' to each side of the equation. 4.555555556x + 5.188271606 + x2 = 26.66666667 + 5.188271606 Reorder the terms: 5.188271606 + 4.555555556x + x2 = 26.66666667 + 5.188271606 Combine like terms: 26.66666667 + 5.188271606 = 31.854938276 5.188271606 + 4.555555556x + x2 = 31.854938276 Factor a perfect square on the left side: (x + 2.277777778)(x + 2.277777778) = 31.854938276 Calculate the square root of the right side: 5.64401792 Break this problem into two subproblems by setting (x + 2.277777778) equal to 5.64401792 and -5.64401792.Subproblem 1
x + 2.277777778 = 5.64401792 Simplifying x + 2.277777778 = 5.64401792 Reorder the terms: 2.277777778 + x = 5.64401792 Solving 2.277777778 + x = 5.64401792 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.277777778' to each side of the equation. 2.277777778 + -2.277777778 + x = 5.64401792 + -2.277777778 Combine like terms: 2.277777778 + -2.277777778 = 0.000000000 0.000000000 + x = 5.64401792 + -2.277777778 x = 5.64401792 + -2.277777778 Combine like terms: 5.64401792 + -2.277777778 = 3.366240142 x = 3.366240142 Simplifying x = 3.366240142Subproblem 2
x + 2.277777778 = -5.64401792 Simplifying x + 2.277777778 = -5.64401792 Reorder the terms: 2.277777778 + x = -5.64401792 Solving 2.277777778 + x = -5.64401792 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.277777778' to each side of the equation. 2.277777778 + -2.277777778 + x = -5.64401792 + -2.277777778 Combine like terms: 2.277777778 + -2.277777778 = 0.000000000 0.000000000 + x = -5.64401792 + -2.277777778 x = -5.64401792 + -2.277777778 Combine like terms: -5.64401792 + -2.277777778 = -7.921795698 x = -7.921795698 Simplifying x = -7.921795698Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.366240142, -7.921795698}
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